Problem: Solve for $x$ : $6x^2 + 24x - 270 = 0$
Dividing both sides by $6$ gives: $ x^2 + {4}x {-45} = 0 $ The coefficient on the $x$ term is $4$ and the constant term is $-45$ , so we need to find two numbers that add up to $4$ and multiply to $-45$ The two numbers $-5$ and $9$ satisfy both conditions: $ {-5} + {9} = {4} $ $ {-5} \times {9} = {-45} $ $(x {-5}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -5) (x + 9) = 0$ $x - 5 = 0$ or $x + 9 = 0$ Thus, $x = 5$ and $x = -9$ are the solutions.